Current Gain in Transistor

In this article we are going to study Current Gain in Transistor of Common Base Transistor and Common Emitter Transistor. Along with the formula of current gain in transistor.

Current gain in Common Base Transistor

• Large signal current gain (α)
• D.C. current gain (α_dc)
• Small signal current gain (α^‘or h_fb).

Large signal current gain (α)

We know

α is known as large signal current gain of a common base transistor. Since I_C and I_E have opposite signs, so α is a positive quantity. The value of α lies between 0.90 to 0.995.

Note. α is not constant. It varies with the emitter current I_E and collector base voltage V_CB.

D.C. current gain (α_dc)

Since I_C >> I_CO,hence eqn. (1) can be written as

which is known as d.c. current gain. α_dc is a positive quantity. Its value is less than 1 as I_C < I_E.

Small signal current gain (α^‘or h_fb).

Small signal current gain is defined as the negative ratio of the small change in collector current (ΔI_C) to small change in emitter current (ΔI_E). That is,

α^‘ is a positive quantity as I_C and I_E have positive signs.

Current gain in a Common Emitter Transistor

• D.C. current gain (β or h_FE)
• Small signal current gain (β^‘ or h_fe).

D.C. current gain (β or h_FE) or Forward current transfer ratio

D.C. current gain of common emitter transistor is defined as the ratio of collector current (I_C) to the base current ( I_B. That is,

The value of β lies between 20 to 200.

Small signal current gain (β^‘ or h_fe).

It is defined as the ratio of small change in collector (ΔI_C) to the small change in base current (ΔI_B) at constant Collector Emitter voltage (V_CE).

β^‘ can be determine from the output characteristics of Common Emitter Configuration.

Relation between Current Gain in Common Base Transistor and Common Emitter Transistor

It is also known as the relation between α and β.

We know, emitter current I_E in term of base current I_B and collector current is given by

Put this value in eqn. (1), We get

Since in active region of transistor, I_B >> I_CO. Hence neglect the term containing I_C0 in eqn. (2)

Collector Current in term of β

Using eqn. (3) in eqn. (2), we get

When base is open circuited (i.e. I_B=0) and junction is reverse biased, then I_C =I_CEO. Hence eqn. (4) becomes

Using eqn. (5) in eqn. (4), we get